Evaluating a Derivative In Exercises 65–72, find and evaluate the derivative of the function at the given point. Use a graphing utility to verify your result. 65. y = r + 8x, (1, 3)
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Q: Finding a Derivative In Exercises 13–32, findthe derivative of the function. y=\sqrt[3]{6 x^{2}+1}
A: y=3(6x2+1)
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A: y=x7
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A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…
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A: x2+y2=64
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A: given f(x) = 4 - x2 point ( 1 , 3 )
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- Finding a Derivative In Exercises 13–32, findthe derivative of the function. y = 5(2 − x3)4In Exercises 63–65, find the domain and range of each composite function. Then graph the composition of the two functions on separate screens. Do the graphs make sense in each case? Give reasons for your answers. Comment on any differences you see. 63. a. y = tan-1 (tan x) b. y = tan (tan-1 x) 64. a. y = sin-1 (sin x) b. y = sin (sin-1 x) 65. a. y = cos-1 (cos x) b. y = cos (cos-1 x)Decomposition of a Composite FunctionIn Exercises 5–12, complete the table. y=(6 x-5)^{4}
- Finding a Derivative In Exercises 13–32, findthe derivative of the function. y=\frac{1}{x-2}In Exercises 11–18, graph each function by making a table of coordinates. If applicable, use a graphing utility to confirm your hand-drawn graph. 11. f(x) = 4" 13. g(x) = ()* 15. h(x) = (})* 17. f(x) = (0.6) 12. f(x) = 5" 14. g(x) = () 16. h(x) = (})* 18. f(x) = (0.8)* %3!Piecewise-Defined FunctionsGraph the functions in Exercises 25–28.
- Ron Larson - Calculus 11th Edition Chp 3.3 - Increasing and Decreasing functions and the first derivative test. Please show all work and explain steps, thank you!Using the definition, calculate the derivatives of the functions in Exercises 1–6. Then find the values of the derivatives as specified. 1. ƒ(x) = 4 - x2; ƒ′(-3), ƒ′(0), ƒ′(1) 2. F(x) = (x - 1)2 + 1; F′(-1), F′(0), F′(2) 3. g(t) = 1 /t2 ; g′(-1), g′(2), g′(sqrt(3)) 4. k(z) = (1 - z )/2z ; k′(-1), k′(1), k′(sqrt(2)) 5. p(u) = sqrt(3u) ; p′(1), p′(3), p′(2/3) 6. r (s) = sqrt(2s + 1) ; r′(0), r′(1), r′(1/2)Mixed Partial DerivativesIn Exercises 55–60, verify that
- In Exercises 73–78, the graph of f is shownin the figure. Sketch a graph of the derivative of f. To print anenlarged copy of the graph, go to MathGraphs.com.image5Ron Larson - Calculus 11th Edition Chp 3.3 Increasing and Decreasing Functions and the First derivative test. Please show all work and steps, thank you!Quantity vs. Rate-of-Change The projected number of senior citizens in the U.S. for the years 1995 through 2030 can be modeled by N(x), million senior citizens, where x is the number of years after 2000. N(x) = 0.03x2 + 0.315x + 34.23 (a) Find the derivative of N(x) and use it to complete the model statement below. (Refer back to Section 3.2 of your text (or ebook) for simple derivative rules.) N'(x)= --select units-- O gives the projected rate at which the number of senior citizens is changing x years after 2000, for the years 1995 through 2030. Use the appropriate function from above to answer questions b through d. (b) What is the projected number of senior citizens in the year 2025? (Round your answers to 3 decimal places.) million senior citizens (c) What is the projected rate of change of the number of senior citizens in 2025? (Round your answers to 3 decimal places.) million senior citizens per year (d) The Census Bureau predicts that in 2030, 20.1% of the U.S. population will…